I am trying to get the arrow from $R$
to $R[x]$
to cooperate with me and go alongside the LHS of the picture.
Here is my MWE:
\begin{tikzcd}
& R \arrow[d, "f"] \arrow[ld, "\phi"', hook'] \arrow[rd, "\phi", hook] \arrow["i", hook', bend right=135]{dd} & \\
R\left\lbrack\frac{1}{r}\right\rbrack \arrow[r, "\exists!F", two heads, dashed, hook] & {\frac{R[x]}{(rx-1)}} \arrow[r, "\exists!G", two heads, dashed, hook] & R\left\lbrack\frac{1}{r}\right\rbrack \\
& {R[x]} \arrow[u, "\pi", two heads] \arrow[ru, "g"'] &
\end{tikzcd}
I'd also like to know how to get the spiral that indicates that the diagram commutes inside the top left and bottom right triangles. See, for example, the below.